Question

*When the axes are rotated through an angle
$\alpha$
find the transformed equation of
$x \cos( \alpha ) + y \sin( \alpha ) = p$
​

Answer 1

Answer:

Transformed equation is X = p

Step-by-step explanation:

When the axes are rotated through an angle alpha, find the transformed equation of xcosalpha + ysin alpha = p

xcosa + ySina = p

The axes are rotated through an angle a

x = X Cosa - Y Sina

y = Xsina + Ycosa

putting these values

(X Cosa - Y Sina) cosa + (Xsina + Ycosa) sina = p

=> X Cos^2 a - Y sinacosa + X sin^2a + Y cosasina = p

=> X(Cos^2a + Sin^2a) = p

=> X = p

Transformed equation is X= p

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Answer 2

Step-by-step explanation:

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